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A comparative study of two optimization approaches for solving bi-level multi-objective linear fractional programming problem

Author

Listed:
  • Rizk M. Rizk-Allah

    (Menoufia University)

  • Mahmoud A. Abo-Sinna

    (Badr University in Cairo)

Abstract

Despite the important role of bi-level multi-objective linear fractional programming (BL-MOLFP) problem for many hierarchical organizations, a very little success has been achieved to deal with this problem. This paper presents a comparative study between two computational approaches, namely fuzzy TOPSIS (technique for order preference by similarity to ideal solution) approach and Jaya (a Sanskrit word meaning victory) approach, for solving BL-MOLFP problem. The fuzzy TOPSIS (FTOPSIS) approach aims to obtain the satisfactory solution of BL-MOLFP problem by using linearization process as well as formulating the membership functions for the distances of positive ideal solution (PIS) and negative ideal solution (NIS) for each level, respectively. In this sense, the deadlock situations among levels are avoided by establishing the membership functions for the upper level decision variables vector with possible tolerances. On the other hand, Jaya algorithm is proposed for solving BL-MOLFP problem based on nested structure scheme to optimize both levels hierarchically. An illustrative example is presented to describe the proposed approaches. In addition, the performances among the proposed approaches are assessed based on ranking strategy of the alternatives to affirm the superior approach. Based on the examined simulation, Jaya algorithm is preferable than the FTOPSIS approach.

Suggested Citation

  • Rizk M. Rizk-Allah & Mahmoud A. Abo-Sinna, 2021. "A comparative study of two optimization approaches for solving bi-level multi-objective linear fractional programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 374-402, June.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:2:d:10.1007_s12597-020-00486-1
    DOI: 10.1007/s12597-020-00486-1
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Rao, R. Venkata & Saroj, Ankit, 2017. "Constrained economic optimization of shell-and-tube heat exchangers using elitist-Jaya algorithm," Energy, Elsevier, vol. 128(C), pages 785-800.
    3. Savita Mishra & Ajit Ghosh, 2006. "Interactive fuzzy programming approach to Bi-level quadratic fractional programming problems," Annals of Operations Research, Springer, vol. 143(1), pages 251-263, March.
    4. R. M. Rizk-Allah & Mahmoud A. Abo-Sinna, 2017. "Integrating reference point, Kuhn–Tucker conditions and neural network approach for multi-objective and multi-level programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 663-683, December.
    5. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    6. Lai, Young-Jou & Liu, Ting-Yun & Hwang, Ching-Lai, 1994. "TOPSIS for MODM," European Journal of Operational Research, Elsevier, vol. 76(3), pages 486-500, August.
    7. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    8. Vyacheslav V. Kalashnikov & Stephan Dempe & Gerardo A. Pérez-Valdés & Nataliya I. Kalashnykova & José-Fernando Camacho-Vallejo, 2015. "Bilevel Programming and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-16, March.
    9. Masatoshi Sakawa & Ichiro Nishizaki, 2012. "Interactive fuzzy programming for multi-level programming problems: a review," International Journal of Multicriteria Decision Making, Inderscience Enterprises Ltd, vol. 2(3), pages 241-266.
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